Problem 16 Easy Difficulty

The figure shows a vector $ a $ in the $ xy $-plane and a vector $ b $ in the direction of $ k $. Their lengths are $ \mid a \mid = 3 $ and $ \mid b \mid = 2 $.

(a) Find $ \mid a \times b \mid $.
(b) Use the right-hand rule to decide whether the components of $ a \times b $ are positive, negative, or 0.

Answer

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02:15

WZ

Wen Z.

02:39

Willis J.

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Video Transcript

mhm. So in this question there is a vector A. That lies in xy plane and there is a vector in the direction of that is in the direction of taxes. Uh And the model is given us three more of these units to, we have to find two things. The first is a cross be more of a Crosby and the second uh point we have to find his components of a Crosby. Uh And so that if they're positive, negative or zero. Now for the first we know that Crosby, there is more of a Crosby people to more of a into more of being to sign it up. No motive is given motive is given. Now we need to find the angle between the you have a trump voter now lies in the xy plane and be lies business direction of taxes. And we know that the angle between the X. Y plane and Alexis's 1980. So we can say that the angle between A and B. Is 1980 so 3090 degree. That is more a more being two scientists, scientists, scientists, scientists. So 320 20 that is 6146 more of A and B is equal to six. Now we'll move to part two, that is, we'll see them components of a Crosby. Now from the right hand rule is here bees here. So a Crosby means we are calling towards this this angle. So while curling towards this angle the across be really perpendicular to both A and B voters. That is, it will lie in this direction well coming and I'm playing right and rules right and stumble across people point in this direction. So we can easily say that this is a cross realizing X and minus one component of the plane. So the X component will be positive because it is lying in Jackson two X component will be bothered. It then we can see that this component will be positive and for the Y component you can see that it is negative. Mhm. Because it is negative part of the way. And now they're confirmed as the eagles beat uh lying the X minus Y axis, but it's uh not lying anywhere. So we can see that the german politics zero. Mhm. Good. Yeah, yeah.